Geoscience Reference
In-Depth Information
Chapter 5
Covering Location Problems
Sergio García and Alfredo Marín
Abstract When deciding where to locate facilities (e.g., emergency points where
an ambulance will wait for a call) that provide a service, it happens quite often that
a customer (e.g., a person) can receive this service only if he/she is under a certain
distance to the closest facility (e.g., the ambulance can arrive in less than 7 min
at this person's home). The problems that share this property receive the name of
covering problems and have many applications (analysis of markets, archaeology,
crew scheduling, emergency services, metallurgy, nature reserve selection, etc.).
This chapter surveys the Set Covering Problem, the Maximal Covering Location
Problem, and related problems and introduces a general model that has as particular
cases the main covering location models. The main theoretical results in this topic
as well as exact and heuristic algorithms are reviewed. A Lagrangian approach to
solve the general model is detailed and, although the emphasis is on discrete models,
some information on continuous covering is provided at the end of the chapter.
Keywords Covering ￿ Discrete optimization ￿ Location
5.1
Introduction
When deciding where to locate facilities (e.g., emergency points where an ambu-
lance will wait for a call) that provide a service, it happens quite often that a
customer (e.g., a person) can receive this service only if he/she is under a certain
distance to the closest facility (e.g., the ambulance can arrive in less than 7 min
at this person's home). The problems that have this property receive the name
of covering problems and, when the previous condition holds, it is said that the
customer is covered.
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